Large regular graphs with no induced 2K2
نویسندگان
چکیده
Let r be a positive integer. Consider r-regular graphs in which no induced subgraph on four vertices is an independent pair of edges. The number v of vertices in such a graph does not exceed 5r/2; this proves a conjecture of Bermond. More generally, it is conjectured that if v > 2r, then the ratio v/r must be a rational number of the form 2 + 1/(2k). This is proved for v/r > 21 _ ~ . The extremal graphs and many other classes of these graphs are described and characterized.
منابع مشابه
The maximum number of edges in 2K2-free graphs of bounded degree
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 8 شماره
صفحات -
تاریخ انتشار 1992